This project focuses on developing new statistical methods, and applying new and existing statistical techniques, to analyze data from laboratory animal studies. The endpoint of interest in a typical carcinogenicity experiment is the tumor incidence rate, which reflects the age-specific rate at which new tumors occur. Unfortunately, most tumors are not observable in live animals; thus, simple estimates of the tumor onset rate are not available. The standard model has three states and three rates at which animals move between states. At any given time, an animal is either alive without a tumor, alive with a tumor, or dead. The rates of transition between these states correspond to the tumor incidence rate, the death rate for animals with a tumor, and the death rate for animals without a tumor. Historically, analyses imposed parametric restrictions on the transition rates, made extreme tumor lethality assumptions, or required additional data such as cause-of-death assessments or interim sacrifices. We have shown previously that a more promising approach is to place constraints on the relationship between the death rates for animals with and without a tumor. This can be done under constant risk difference or constant risk ratio assumptions. When few tumors are observed, these methods can be computationally unstable or overly sensitive. We have developed a Bayesian approach that uses data augmentation and Gibbs sampling to ease the problems that arise when tumor response data are sparse. These Bayesian methods incorporate additional information such as expert opinions and historical data. We also have developed flexible estimates for the tumor incidence funtion. These estimates automatically adjust for survival and tumor lethality, and they only require a minimal amount of sacrifice data.